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We measured the covariance matrix of the fields generated in an integrated third-order optical parametric oscillator operating above threshold. We observed up to $(2.3 \pm 0.3)$ dB of squeezing in amplitude difference, inferred $(4.9 \pm 0.7)$ dB of on-chip squeezing, while an excess of noise for the sum of conjugated quadratures hinders the entanglement. The degradation of amplitude correlations and state purity for the increasing of the pump power is consistent with the observed growth of the phase noise of the fields, showing the necessity of strategies for phase noise control aiming at entanglement generation in these systems., Comment: main text: 4 pages, 6 figures; supplemental material: 13 pages, 15 figures

The nilpotent graph of a group $G$ is the simple and undirected graph whose vertices are the elements of $G$ and two distinct vertices are adjacent if they generate a nilpotent subgroup of $G$. Here we discuss some topological properties of the nilpotent graph of a finite group $G$. Indeed, we characterize finite solvable groups whose closed neighborhoods are nilpotent subgroups. Moreover, we study the connectivity of the graph $\Gamma(G)$ obtained removing all universal vertices from the nilpotent graph of $G$. Some upper bounds to the diameter of $\Gamma(G)$ are provided when $G$ belongs to some classes of groups., Comment: Added a reference to the paper by Burness, Lucchini, and Nemmi

Conditional symmetries were introduced by Levi and Winternitz in their 1989 seminal paper to deal with nonlinear PDEs. Here we discuss their application in the framework of ODEs, and more specifically Dynamical Systems; it turns out they are closely related to two established -- albeit maybe less widely known -- concepts, i.e. orbital symmetries and configurational invariants. The paper is devoted to studying the interplay of these notions, and their application in the study of Dynamical Systems, with special attention to invariant manifolds of these., Comment: 35 pages; V3: minor TeX issues solved. Published in OCNMP

The nonlinear interaction of a microresonator pumped by a laser has revealed complex dynamics including soliton formation and chaos. Initial studies of coupled-resonator systems reveal even more complicated dynamics that can lead to deterministic modelocking and efficient comb generation. Here we perform theoretical analysis and experiments that provide insight into the dynamical behavior of coupled-resonator systems operating in the normal group-velocity-dispersion regime. Our stability analysis and simulations reveal that the strong mode-coupling regime, which gives rise to spectrally-broad comb states, can lead to an instability mechanism in the auxiliary resonator that destabilizes the comb state and prevents mode-locking. We find that this instability can be suppressed by introducing loss in the auxiliary resonator. We investigate the stability of both single- and multi-pulse solutions and verify our theoretical predictions by performing experiments in a silicon-nitride platform. Our results provide an understanding for accessing broad, efficient, relatively flat high-power mode-locked combs for numerous applications in spectroscopy, time-frequency metrology, and data communications.

Silicon nitride (SiN) formed via low pressure chemical vapor deposition (LPCVD) is an ideal material platform for on-chip nonlinear photonics owing to its low propagation loss and competitive nonlinear index. Despite this, LPCVD SiN is restricted in its scalability due to the film stress when high thicknesses, required for nonlinear dispersion engineering, are deposited. This stress in turn leads to film cracking and makes integrating such films in silicon foundries challenging. To overcome this limitation, we propose a bilayer waveguide scheme comprised of a thin LPCVD SiN layer underneath a low-stress and low-index PECVD SiN layer. We show group velocity dispersion tuning at 1550nm without concern for filmcracking while enabling low loss resonators with intrinsic quality factors above 1 million. Finally, we demonstrate a locked, normal dispersion Kerr frequency comb with our bilayer waveguide resonators spanning 120nm in the c-band with an on-chip pump power of 350mW.

Optical networks are the leading platform for the transfer of information due to their low loss and ability to scale to many information channels using optical frequency modes. To fully leverage the quantum properties of light in this platform, it is desired to manipulate higher-dimensional superpositions by orchestrating linear, beamsplitter-type interactions between several channels simultaneously. We propose a method of achieving simultaneous, all-to-all coupling between N optical frequency modes via N-way Bragg-scattering four-wave mixing. By exploiting the frequency degree of freedom, additional modes can be multiplexed in an interaction medium of fixed volume and loss, avoiding the introduction of excess noise. We generalize the theory of the frequency-encoded two-mode interaction to N modes under this four-wave mixing approach and experimentally verify the quantum nature of this scheme by demonstrating three-way multiphoton interference. The two input photons are shared among three frequency modes and display interference differing from that of two classical (coherent-state) inputs. These results show the potential of our approach for the scalability of photonic quantum information processing to general N-mode systems in the frequency domain.

The study of verbal subgroups within a group is well-known for being an effective tool to obtain structural information about a group. Therefore, conditions that allow the classification of words in a free group are of paramount importance. One of the most studied problems is to establish which words are concise, where a word $w$ is said to be concise if the verbal subgroup $w(G)$ is finite in each group $G$ in which $w$ takes only a finite number of values. The purpose of this article is to present some results, in which a hierarchy among words is introduced, generalizing the concept of concise word.

Alzheimer's disease (AD) and sleep disorders exhibit a close association, where disruptions in sleep patterns often precede the onset of Mild Cognitive Impairment (MCI) and early-stage AD. This study delves into the potential of utilizing sleep-related electroencephalography (EEG) signals acquired through polysomnography (PSG) for the early detection of AD. Our primary focus is on exploring semi-supervised Deep Learning techniques for the classification of EEG signals due to the clinical scenario characterized by the limited data availability. The methodology entails testing and comparing the performance of semi-supervised SMATE and TapNet models, benchmarked against the supervised XCM model, and unsupervised Hidden Markov Models (HMMs). The study highlights the significance of spatial and temporal analysis capabilities, conducting independent analyses of each sleep stage. Results demonstrate the effectiveness of SMATE in leveraging limited labeled data, achieving stable metrics across all sleep stages, and reaching 90% accuracy in its supervised form. Comparative analyses reveal SMATE's superior performance over TapNet and HMM, while XCM excels in supervised scenarios with an accuracy range of 92 - 94%. These findings underscore the potential of semi-supervised models in early AD detection, particularly in overcoming the challenges associated with the scarcity of labeled data. Ablation tests affirm the critical role of spatio-temporal feature extraction in semi-supervised predictive performance, and t-SNE visualizations validate the model's proficiency in distinguishing AD patterns. Overall, this research contributes to the advancement of AD detection through innovative Deep Learning approaches, highlighting the crucial role of semi-supervised learning in addressing data limitations., Comment: 12 pages, 14 figures. Submitted to IEEE Biomedical and Health Informatics for publication

High harmonic generation traditionally combines ~100 near-infrared laser photons, to generate bright, phase matched, extreme ultraviolet beams when the emission from many atoms adds constructively. Here we show that by guiding a mid-infrared femtosecond laser in a high pressure gas, ultrahigh harmonics can be generated up to orders > 5000, that emerge as a bright supercontinuum that spans the entire electromagnetic spectrum from the ultraviolet to > 1.6 keV, allowing in-principle the generation of pulses as short as 2.5 attoseconds. The multi-atmosphere gas pressures required for bright, phase matched emission also supports laser beam self-confinement, further enhancing the x-ray yield. Finally, the x-ray beam exhibits high spatial coherence, even though at high gas density, the recolliding electrons responsible for high harmonic generation encounter other atoms during the emission process., Comment: 32 pages, 9 figures (4 in main text, 5 in supplemental materials)

We present a version of the classical Moran model, in which mutations are taken into account; the possibility of mutations was introduced by Moran in his seminal paper, but it is more often overlooked in discussing the Moran model. For this model, fixation is prevented by mutation, and we have an ergodic Markov process; the equilibrium distribution for such a process was determined by Moran. The problems we consider in this paper are those of first hitting either one of the ``pure'' (uniform population) states, depending on the initial state; and that of first hitting times. The presence of mutations leads to a nonlinear dependence of the hitting probabilities on the initial state, and to a larger mean hitting time compared to the mutation-free process (in which case hitting corresponds to fixation of one of the alleles)., Comment: 22 pages, 8 figures

Advances in gene sequencing have enabled in silico analyses of microbial genomes and have led to the revision of concepts of microbial taxonomy and evolution. We explore deficiencies in existing multiple sequence global alignment algorithms and introduce a new indexing scheme to partition the dynamic programming algorithm hypercube scoring tensor over processors based on the dependency between partitions to be scored in parallel. The performance of algorithms is compared in the study of rpoB gene sequences of Mycoplasma species.

Self-injection locking techniques for stabilizing lasers have been developed using passive cavities to increase the effective lifetime of the laser cavity, thereby reducing the linewidth of the laser. We propose and demonstrate a new technique based on nonlinear self-injection locking (N-SIL) which we implement via feedback from the gain-narrowed Stokes mode of a fiber Brillouin oscillator. By blue-shifting the Stokes field back to its pump frequency with an electro-optic modulator we realize recursive linewidth reduction that eliminates the phase drift caused by spontaneous emission noise. The fundamental linewidth limit is set by the spontaneous emission limit of the nonlinear oscillator, far lower than the spontaneous emission limit of a semiconductor laser. We demonstrate the power of this approach by achieving sub-hertz fundamental linewidth from the output of a commercial DFB laser and noise performance that significantly exceeds that of conventional SIL. We also and propose alternative fully-integrated designs in CMOS-compatible photonic platforms that allow for highly compact and robust implementations.

In a recent paper we have classified scalar Ito equations which admits a standard symmetry; these are also directly integrable by the Kozlov substitution. In the present work, we consider the diffusion (Fokker-Planck) equations associated to such symmetric Ito equations., Comment: 24 pages, no figures